Kurako is Yuzu's elder sister, teacher and head of the Miko council. So if you think about she has authority over Yuzu on at least three levels. Kurako is more experienced than the rest of the Miko and is capable of doing more. However this does not mean she can do everything. If she could then I'd probably get bored of the series. Kurako is a serious woman and likes to make sure that Yuzu and the others take their training seriously. Mainly because she is a very protective person.
Attacks

Prayer of Three Sisters (Made up name): Kurako and her sisters begin to say a prayer together. After the prayer is done each yells out a word. Probably related to their part of the prayer. Kurako's word is "shield" At this point a circle of white energy destroys the enemy.

Bind of Earth: Kurako creates a gold ring of energy to imprison the enemy. If you've seen other rings of energy in anime, you can probably guess how successful this attack is.

Flaming Arrow of God: A Standard attack. Where by the user adds an elemental property (fire) to a weapon (arrow) to damage the enemy with it (buring them).